Description of Global Analysis

For the analysis, I consider the K-band data and select 10 calibration fields which have data from both Northern and Southern 2MASS facilities. The fields are listed in Table 1 (where the coordinates of a field are those of the fiducial standard in the field).

 

Table 1: Calibration fields observed by both Northern and Southern 2MASS facilities. Coordinates of each field (listed in degrees) are those of the fiducial standard in the field.

Field	R.A. (J2000)	Dec. (J2000)
90004	28.657154	+0.717208
90021	6.102505	-1.972259
90565	246.677917	+5.872222
90808	285.480833	-4.486667
90813	310.271250	-5.061944
90860	185.413750	-0.120278
90867	220.241667	-0.463056
90868	225.109925	-0.658013
90893	349.541667	+0.548889
92202	331.399018	-11.074560

The dataset is divided into two subsets: the subset containing only data from South and the one containing only data from North. For each subset, the global calibration solution (LSC0, see Nikolaev 1998) is calculated producing two separate solutions for North and South. Each solution is represented by nightly photometric parameters (zero points and slopes) and the atmospheric extinction coefficient A_K. I then use both Northern and Southern solutions to obtain calibrated magnitudes for 50 field stars in each of the 10 calibration fields. The magnitudes of the field stars are ranging approximately from 9th to 14th magnitude. For every field star I obtain both the mean calibrated magnitude and the standard deviation from the mean based on all individual observations of the star. Figures 1 and 2 characterize both solutions in terms of pooled root variance for all field stars in every field. Note the number of ``outliers'' with $\sigma > 0.1$ in both solutions. I analyze the outliers in the Appendix A.

The Southern solution is derived from 966 observations of the fiducial standards and the overall goodness of fit is given by the mean squared norm of the residual vector $R = (\sum r_i^2)/(N-M)$, where N is the number of observations and M is the number of free parameters. The Northern solution is derived from 3,662 observations of the fiducial standards. The calibration solutions are summarized in Table 2, where I list the atmospheric extinction coefficients

 

Table 2: Atmospheric extinction coefficients and mean squared norms of the residual vectors from the global photometric solution LSC0. The extinction coefficients are in magnitudes per unit airmass. CTIO values from Frogel 1998 are listed for comparison.

Band	Hemisphere	$A_\lambda$	Residual, R	$A_\lambda$, CTIO
J	North	$0.117\pm0.003$	$8.10 \times 10^{-4}$
J	South	$0.106\pm0.009$	$2.16 \times 10^{-3}$	$0.100\pm0.024$
H	North	$0.039\pm0.003$	$1.03 \times 10^{-3}$
H	South	$0.079\pm0.009$	$2.06 \times 10^{-3}$	$0.055\pm0.021$
K	North	$0.079\pm0.004$	$1.47 \times 10^{-3}$
K	South	$0.059\pm0.006$	$9.14 \times 10^{-4}$	$0.085\pm0.018$

(which are free parameters of the model) and the residuals R for all three bands. The atmospheric extinction is likely to change over the year (see Weinberg & Nikolaev 1998, Frogel 1998), however, in the global calibration model it is a constant in each band. The value $\sqrt{R}$ is the mean photometric precision of the global solution.